A PA28 pilot at a VFR cruising altitude reported a NMAC with a C172 flying directly underneath them.

Narrative

While flying on a heading of 013 at an altitude of 3;500 feet MSL; I observed Aircraft Y on my ADS-B In display at my 10 o'clock position; approximately 2 miles away and 700 feet below. I gained visual contact with the aircraft initially. It briefly veered off but then re-establihed a trajectory that would have led to a collision had we been at the same altitude. At that point; I lost visual contact; with the other aircraft now 500 feet beneath me.Recognizing the potential conflict; I initiated a climb at 500 fpm. Aircraft Y had turned to match my course exactly and was flying directly beneath me; resulting in a vertical separation of 500-550 feet. I remained concerned due to our proximity and the lack of visual contact; especially since Aircraft Y--a Cessna 172--is a high-wing aircraft; while I was flying a low-wing aircraft. Given our relative positions; neither pilot would likely be able to see the other.I attempted to contact Aircraft Y on the CTAF for the nearest airport (ZZZ) without success; then switched to the CTAF for ZZZ1. The flight instructor responded and indicated they had me on ADS-B; suggesting there was no issue. I expressed that ADS-B In is not fully reliable and/or accurate in real time and that I had to climb to avoid a collision. Before I could coordinate to deconflict the situation; the instructor became argumentative; insisting they had remained within their designated training area and never exceeded 2;500 MSL. However; flight tracking via FlightAware confirms Aircraft Y did actually exceed that stated altitude during this sequence of events.Following the discussion about ADS-B limitations; the instructor then claimed they also had visual contact with my aircraft the entire time; an assertion that is implausible given our respective aircraft types and positions.Eventually; Aircraft Y turned northwest and ceased to fly directly beneath me. Thanks to my climb; there was approximately 1;200 feet of vertical separation at this point.Key Concerns:- Inappropriate Reliance on ADS-B In for VFR Separation: The instructor appeared to rely solely on ADS-B data; and after being called on this; he later claimed visual contact in a situation where such contact would have been improbable due to wing configuration and relative altitude.- Lack of Radio Coordination During a Conflict Situation: Aircraft Y entered a direct conflict with my flight path without prior radio contact or coordination with me; increasing collision risk in shared airspace.- Failure to Monitor Relevant CTAF Frequencies: The aircraft did not monitor the CTAF for the three closest airports within their designated (and alleged) training area; limiting situational awareness and communication opportunities. Contact was only possible because their radio remained set to the CTAF for ZZZ1; which was approximately 12.5 NM away.